Having problems with translating negative edges
The origin remains unchanged when the object is modified in Edit mode. To move the origin, switch to Object mode and use the button Tool Shelf>Set Origin (or Ctrl-Shift-Alt C)
Possibly, check the Snap during transform options (the magnet icon or Shift-Tab)


To reshape your wedge, start from a cube, switch to Edit mode, disable the snapping, select the vertices to be moved, enable the 3D manipulator in Translate mode and drag the arrow in the 3D view.